Tangential Velocity, Frames, and the Speed of Light

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Discussion Overview

The discussion revolves around the concept of tangential velocity and the implications of different frames of reference in the context of two spacecraft approaching each other at relativistic speeds. Participants explore the observer's perspective from a rotating craft and the measurements of velocities of the two ships, considering both inertial and non-inertial frames.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether the velocity of Ship A can be assumed to be zero in their frame, given they cannot measure it directly.
  • Another participant challenges the clarity of the scenario, emphasizing the need for a defined frame of reference and questioning the inability to measure the velocities of both ships.
  • A later reply discusses the complexities of using a rotating coordinate system, noting that it is a non-inertial frame and that different coordinate systems can be constructed where various objects are at rest.
  • One participant proposes a hypothetical scenario where both ships are traveling at the speed of light, raising questions about the measurements of their speeds from the observer's perspective.
  • There is a correction regarding the geometry of the situation, with a participant pointing out the error in the angle of the triangle described by the observer.
  • Another participant acknowledges the need for acceleration in the observer's rotational velocity to maintain the position of Ship A relative to the observer.
  • One participant expresses confusion about the geometry, clarifying that they meant a right triangle instead of an equilateral triangle.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the measurements of velocities or the implications of the rotating frame. Multiple competing views and uncertainties remain regarding the definitions and calculations involved.

Contextual Notes

The discussion includes limitations related to the assumptions about frames of reference, the nature of non-inertial frames, and the mathematical steps involved in calculating velocities. The scenario also relies on hypothetical conditions that may not align with established physical laws.

Nishmaster
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Hello gurus,

I have a mental experiment that I'm wrangling with.

Assume for a moment that two craft (Ship A and Ship B) are approaching each other at a significant fraction of c. Let us also assume that I, the observer, am in a stationary craft a large distance away rotating with the plane given by the vector of the two approaching craft, keeping one of them (Ship A) stationary in the center of my field of vision.

I have two questions:

1. Since I have no way of measuring the velocity of Ship A in my frame, is it assumed to be zero?

2. What would I measure as the velocity of Ship B?

I'm no mathematician of this level, but by all means don't dumb it down for me, as I'm really trying to pick some of this up. :smile:
 
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You haven't specified the scenario properly because

.. I, the observer, am in a stationary craft ..

has no meaning unless you say in which frame of reference you are stationary. Presumably you mean to take your own ship as the stationary frame ?

Also, I'm puzzled as to why you think you can't measure the velocity of the other ships.

If you can measure one, why not the other ?
 
Nishmaster said:
1. Since I have no way of measuring the velocity of Ship A in my frame, is it assumed to be zero?

2. What would I measure as the velocity of Ship B?
In what coordinate system are you asking for the velocities of the ships? If you want a coordinate system where every part of your craft is at rest, this would be a rotating coordinate system, and thus a non-inertial one, and there isn't really a single coordinate system which is "the" rest frame of a non-inertial observer, you can construct a variety of different coordinate systems where any given non-inertial object is at rest. On the other hand, if you want the inertial frame where the center of your craft is at rest while the rest of it rotates around it, then your own rotation is irrelevant to calculating the velocities of the ships in this frame.
 
Yes, the frame here I am referring to would be a rotating coordinate system, where every part of my craft is at rest.

I guess my more overarching question perhaps is this:

Ignore the fact that ships have mass for a second and assume Ship A and B are both traveling at 1c. My observer craft is at 1 light second from the collision point, and each ship is also 1 light second from the collision point. So now, I have an equilateral triangle between myself, the collision point, and Ship A, if that makes any sense.

I can find that at the start of this experiment I am 45 degrees from where I will be when the ships collide, thus my rotational velocity is roughly 14.32 rad/s. Since I am rotating with respect to Ship A, I would measure using Pythagoras that Ship A is 1.41 (sqrt(2)) light seconds away at the start, and 1 light second away at the end, and thus is moving toward me at .41 light seconds/s.

My question is: What would I measure as the speed of Ship B? Would it be greater than c?

Something I just realized is that I suppose my rotational velocity is not constant. It would have to be accelerating to keep Ship A stationary with respect to the x component of its vector.
 
Nishmaster said:
Yes, the frame here I am referring to would be a rotating coordinate system, where every part of my craft is at rest.
Then, as Mintz114 said, you are not in an enertial frame of reference and the usual formulas for special relativity do not apply.

I guess my more overarching question perhaps is this:

Ignore the fact that ships have mass for a second and assume Ship A and B are both traveling at 1c. My observer craft is at 1 light second from the collision point, and each ship is also 1 light second from the collision point. So now, I have an equilateral triangle between myself, the collision point, and Ship A, if that makes any sense.

I can find that at the start of this experiment I am 45 degrees from where I will be when the ships collide
How do you do that? The angles in an equilateral triangle are 60 degrees, not 45 degrees.

, thus my rotational velocity is roughly 14.32 rad/s. Since I am rotating with respect to Ship A, I would measure using Pythagoras that Ship A is 1.41 (sqrt(2)) light seconds away at the start, and 1 light second away at the end, and thus is moving toward me at .41 light seconds/s.

My question is: What would I measure as the speed of Ship B? Would it be greater than c?

Something I just realized is that I suppose my rotational velocity is not constant. It would have to be accelerating to keep Ship A stationary with respect to the x component of its vector.
 
:rolleyes:

Sorry, I have not yet had my coffee for the day. What I meant was a right triangle.
 

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